A 3.5 Factor, Hyperluminous Neutrinos and Infinitely Fast ProcessesFirst let's talk about a 3.5 factor in my theory. When developing the theory, I as everybody else, took clues from reality. A theory has to be self-consistent and consistent with reality. I realized that deriving the theory just by looking at cross-sections of an light-speed expanding hypersphere wasn't in line with the standard way of thinking. One normally thinks about a force, being communicated through space and distance... so the field will naturally be diluted by the area though which it is diffusing..:)
If I were to use that kind of reasoning in my theory, I would have a much harder time thinking about the physics... in addition, I noticed that deriving a physical theory in an noncompact 4D spatial manifold using cross-sections yielded the same laws as deriving a theory using fields in a 3D-manifold. Of course, this has implications on the meaning of a delocalized mode. If one considers a photon being emitted by a molecule. That photon at long distances, can be thought as being carried by a spherical wave. Of course, that wave collapses immediately at the time that photon is absorbed by another molecule. What is the meaning of distributing it throughout space, just to collapse it instantaneously during absorption. One doesn't have to remind you, that this goes against Relativity. It is a form of instantaneous communication in the same way as the process of spin correlation in correlated-at-origin photons.
These are hard questions about the Nature of Photons. In my theory, photons are spatial modulations of the dilaton wave-generator (dilator). The same difficulties arises. So the idea that interaction has to have a representation as diffusive process on an area or volume is hardly clear. The derivation by cross-section (2-Dimensional) circumference might be closer to the actual physics than a diffusion of a field through an expanding area.
I decided to go against fields (Fields of Dreams - my prior posting) as static properties of space. Instead I decided that space should not be subject to a static strain, but it should be flexible and be the medium for waves.
In a cross-section analysis, I made the 'field" (wave amplitude) to decay inversely proportional to the number of nodes. The same reasoning using fields, would imply that the field would decay inversely to the square of the distance...:)
There is more than just a predilection and sense of aesthetics in play here. You cannot create a theory of everything by introducing more things (more constructs - force, field, mass, etc). It is just a Rube Goldberg Machine....:)
In deriving the equations, I considered how much should the field decay at each de Broglie step. There were three identical cross-sections (3) and there was a linear dimension along the radial direction where the dilaton field would also propagate. At the time, ridding a subway, shaking left and right, it made sense. Now it makes less sense and might require the addition of an extra parameter (there is almost no parameters in my theory).
That parameter would relate 4D Mass to 3D Mass. We always knew that to go from 3D to 4D required a strong analogical mind... :) For 3D to 4D gravitational masses, my initial 1:2 relationship is fine. When I move to 4D electromagnetic mass, extra parametrization might be required. When I have time, I will develop this further. This shouldn't be a problem to any physicist worth their salt....after all, whenever it was convenient, infinite became finite (renormalization) in our current physical theories..etc.
When I have time, I will revisit this subject.
Hyperluminous NeutrinosIn my theory, an electron neutrino (related to Neutron decay), maps to a two dimensional wave propagating in the 4D spatial manifold. The neutrino is responsible for rotating the dilaton within the 3D Hyperspherical Hypersurface (3D Universe).
Since Neutrino and Light (photons) are elastic propagating deformations of space in my theory, one would expect them to travel at different speeds - think dispersion..:). Neutrinos are transversal waves and photons are longitudinal waves. Under normal materials, transversal waves are faster, which would make Neutrinos Hyperluminous.
Faster than the speed of light neutrinos were "observed" in an experiment Opera, just to be denied a few months later. The poor scientist Prof Antonio Ereditato who dared to Challenge Einstein's Theory, had to resign. Of course, I've never considered that neutrinos and light traveled at the same speed and still believe neutrinos are faster, just because of their topology (transversal spatial deformation waves).
Of course, I don't have a place to resign, so I can say anything.. and that is a good thing. Backing me up, is another physical observation . The early arrival of neutrinos when a Supernova exploded (Supernova 1987a,) someplace else. Neill deGrasse Tyson, who has a place from which to resign, cautiously suggested that there was a way to explain why a photon (which has no mass) should be slowed more by a gravitational field than a neutrino which supposedly might have some mass...:)
I don't know how he does it... The mental contortion to avoid stating the obvious - that Neutrinos - whatever they are, might travel faster than the speed of light... after all they arrived earlier than the light from that Supernova...:) The difference in speed is 0.0000003%, something Opera couldn't never detect.
That is the problem with idolatry... Einstein was good, very good... but if we keep him in a pedestal, we are not going anywhere.
Infinitely Fast Processes
Ask questions while I still might know the answers...:)